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Collections of Statements Related to Domination Parameters in Graphs

D. R. Robert Joan*, Y. Sheeja**

* Assistant Professor of Mathematics in Christian College of Education, Marthandam, Tamilnadu, India.

** Assistant Professor, Department of mathematics, M.E.T. College of Education, Chenbagaramanputhoor, Tamilnadu, India.

Periodicity:January - March'2014
DOI : https://doi.org/10.26634/jmat.3.1.2938

Abstract

A dominating set D ⊆ V is said to be a nilprivate neighbour dominating set if, for every vertex u in D has no private neighbour in V-D. The nilprivate neighbour domination number γ_npn(G) is the minimum cardinality of a nilprivate npn neighbour dominating set. A dominating set D⊆ V of a graph G is a non-split dominating set if the induced sub-graph is connected. The non-split domination number γ_ns(G) is the minimum cardinality of a non-split dominating set of G. A dominating set D ⊆ V of a graph G is a strong non-split dominating set if the induced sub-graph is complete. The strong non-split domination number sns(G) is the minimum cardinality of a strong non-split dominating set of G. The dominating set D ⊆ V of a graph G is a vertex set dominating set if for any set S ⊆V-D, there exists a vertex vD such that the induced sub-graph is connected.The vertex set domination number γ_vs(G) is the minimum cardinality of a vs vertex set dominating set of G. A dominating set D of a graph G = (V, E) is a strong non-split dominating set if the induced sub-graph is complete. The strong non-split domination number γ_sns(G) of G is the minimum cardinality of a strong sns non-split dominating set of G. Here, the authors state some definitions and statements related to the Nilprivate neighbour domination and strong non-split domination number in graphs. In conclusion, the authors state the domination of strong non-split domination graphs.

Keywords

Dominating Set, Total Dominating Set, Global Dominating Set, Split Dominating Set, Strong Split Dominating Set, Nilprivate Neighbour, Nil Private Neighbour Dominating Set.

How to Cite this Article?

Joan, D. R. R., and Sheeja, Y. (2014). Collections Of Statements Related To Domination Parameters In Graphs. i-manager’s Journal on Mathematics, 3(1), 7-13. https://doi.org/10.26634/jmat.3.1.2938

References

[1]. Cockayne, E.J., Dawes, R.M. & Hedetniemi, S. T. (1977). Total domination in graphs. Networks, Vol.10, pp.211-219.

[2]. Haynes, T. W., Hedetniemi, S.T., & Slater, P.J. (1998). Fundamentals of Domination in Graphs. Marcel Dekker, Inc. New York,

[3]. Joseph, J., & Arumugam, S. (1992). On connected cut free domination in graphs. Indian Journal of Pure and Applied Mathematics, Vol.23, pp.643-647.

[4]. Kulli, V.R., & Janakiram, B. (1997). The Split domination number of a graph. Graph theory notes of New York, New York: pp.16 - 19.

[5]. Sampathkumar, E. (1989). The global domination number of a graph. Journal of Mathematics and Physical Science, Vol.23, pp.377-385.

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